MinT - Information on Result #1647116

Information on Result #1647116

Linear OOA(3¹⁸⁷, 1195750, F₃, 5, 20) (dual of [(1195750, 5), 5978563, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁷, 1195750, F₃, 4, 20) (dual of [(1195750, 4), 4782813, 21]-NRT-code), using

OOA 4-folding [i] based on linear OA(3¹⁸⁷, 4783000, F₃, 20) (dual of [4783000, 4782813, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁸⁷, 4783001, F₃, 20) (dual of [4783001, 4782814, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(16) [i] based on
    1. linear OA(3¹⁸³, 4782969, F₃, 20) (dual of [4782969, 4782786, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(3¹⁵⁵, 4782969, F₃, 17) (dual of [4782969, 4782814, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁸⁸, 1195750, F₃, 5, 20) (dual of [(1195750, 5), 5978562, 21]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁸⁷, 597874, F₃, 25, 20) (dual of [(597874, 25), 14946663, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row